Title: Expanders, groups and applications

                 	Eyal Rozenman
   Center for the Mathematics of Information
       California Institute of Technology

Abstract:  Last week we defined expanders and how to get them from groups.
In the upcoming talk I'll present some beautiful applications:

- Constructions of good error correcting codes, and the relation to
expanders on the group (Z_2)^n.
- Deterministic simulation of a random walk on a graph and its application
for solving connectivity questions on the graph.
- How to generate a random element in a group given only generators of the
group, and the relation to expanders on the group of symmetries of free
groups. 
- The Banach-Tarski Paradox and the relation to embedding expanders in the
group of 3-dimensional rotations